IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p571-d512404.html
   My bibliography  Save this article

Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments

Author

Listed:
  • Marat Akhmet

    (Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey)

  • Duygu Aruğaslan Çinçin

    (Department of Mathematics, Süleyman Demirel University, Isparta 32260, Turkey)

  • Madina Tleubergenova

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan)

  • Zakhira Nugayeva

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan)

Abstract

This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches.

Suggested Citation

  • Marat Akhmet & Duygu Aruğaslan Çinçin & Madina Tleubergenova & Zakhira Nugayeva, 2021. "Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:571-:d:512404
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/571/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/5/571/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marat Akhmet & Madina Tleubergenova & Mehmet Onur Fen & Zakhira Nugayeva, 2020. "Unpredictable Solutions of Linear Impulsive Systems," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    2. Marat Akhmet & Madina Tleubergenova & Zakhira Nugayeva, 2020. "Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    3. Huang, Zhenkun & Wang, Xinghua & Xia, Yonghui, 2009. "A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1121-1131.
    4. Itamar Daniel Landau & Haim Sompolinsky, 2018. "Coherent chaos in a recurrent neural network with structured connectivity," PLOS Computational Biology, Public Library of Science, vol. 14(12), pages 1-27, December.
    5. Samuel P Muscinelli & Wulfram Gerstner & Tilo Schwalger, 2019. "How single neuron properties shape chaotic dynamics and signal transmission in random neural networks," PLOS Computational Biology, Public Library of Science, vol. 15(6), pages 1-35, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2023. "Compartmental Unpredictable Functions," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    2. Pengfei Guo & Yunong Zhang, 2022. "Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-," Mathematics, MDPI, vol. 10(9), pages 1-27, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akhmet, Marat & Tleubergenova, Madina & Zhamanshin, Akylbek, 2024. "Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Duan, Dongli & Wu, Xixi & Bai, Xue & Yan, Qi & Lv, Changchun & Bian, Genqing, 2022. "Dimensionality reduction method of dynamic networks for evolutionary mechanism of neuronal systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    3. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:571-:d:512404. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.